Question

3. Wage negotiations with reversed bargaining power: Reconsider the wage ne- gotiation model at United from class, but assume now that United has the bargaining power and is making a take-it-or-leave-it wage offer w to its pilots. United's profits (before wages) are 11, which is known to everybody. The pilots' outside option, when rejecting United's wage offer, on the other hand is only known to the pilots, while United believes that it equals 6,7,8,9 or 10 with equal probability. United's payoff equals 11-w if the pilots accept the offer, and 0 if the pilots reject the offer Other than those discussed in class 2Assume that workers (and the firm) choose to sign the contract when they are indifferent. Price MB MB MC Quantity (a) Calculate for each level of w є {6, 7, 8, 9, 10), the probability the pilots will accept the offer, and expected profits to United.3 (b) Which level of w maximizes expected profits? (c) Is the resulting outcome (when United maximizes profits) efficient?

Answer 1

Solution:A) Let A=event that the pilot accepts the wage offer made by United and P = United's payoff

If w=6; P(A1) =1/5

E(P1)=1/5*(11-6) + 4/5*0

=1

If w=7; P(A2)=1/5

E(P2)=1/5*(11-7)

=4/5

If w=8

E(P3)=1/5*(11-8)

=3/5

If w=9

E(P4)=1/5*(11-9)

=2/5

If w=10

E(P5)=1/5*(11-10)

=1/5

B) The expected profit of United is maximized if it pays the pilots wage, (w=6)

C) It is not the efficient wage since the pilots may reject the offer if he gets higher wage outside. The the expected profit of United will be equal to 0.